Algebra and Trigonometry: Structure and Method, Book 2
Algebra and Trigonometry: Structure and Method, Book 2
2000th Edition
ISBN: 9780395977255
Author: MCDOUGAL LITTEL
Publisher: McDougal Littell
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Chapter 4.6, Problem 51WE
To determine

To Prove:

To show that x2+(k+1)x+k is reducible for all positive integers k.

Expert Solution & Answer
Check Mark

Explanation of Solution

Given information:

The given polynomials is x2+(k+1)x+k .

Consider the polynomial x2+(k+1)x+k ,

In order to factor a polynomial, we need 2 numbers that add up to the co-efficient of the linear term and multiply to equal the product of the co-efficient of the quadratic term and constant.

For instance, consider the polynomial x2+4x+3 , two numbers that add up to 4 and multiply to 3 are 3 and 1. Therefore, this can be factored to (x+3)(x+1) .

Therefore, we can conclude for all the cases that x2+(k+1)x=k is reducible for all positive k since it can be simplified to (x+k)(x+1) .

Hence, the polynomial x2+(k+1)x+k is reducible for all positive integers k.

Chapter 4 Solutions

Algebra and Trigonometry: Structure and Method, Book 2

Ch. 4.1 - Prob. 11OECh. 4.1 - Prob. 12OECh. 4.1 - Prob. 13OECh. 4.1 - Prob. 14OECh. 4.1 - Prob. 15OECh. 4.1 - Prob. 16OECh. 4.1 - Prob. 17OECh. 4.1 - Prob. 18OECh. 4.1 - Prob. 1WECh. 4.1 - Prob. 2WECh. 4.1 - Prob. 3WECh. 4.1 - Prob. 4WECh. 4.1 - Prob. 5WECh. 4.1 - Prob. 6WECh. 4.1 - Prob. 7WECh. 4.1 - Prob. 8WECh. 4.1 - Prob. 9WECh. 4.1 - Prob. 10WECh. 4.1 - Prob. 11WECh. 4.1 - Prob. 12WECh. 4.1 - Prob. 13WECh. 4.1 - Prob. 14WECh. 4.1 - Prob. 15WECh. 4.1 - Prob. 16WECh. 4.1 - Prob. 17WECh. 4.1 - Prob. 18WECh. 4.1 - Prob. 19WECh. 4.1 - Prob. 20WECh. 4.1 - Prob. 21WECh. 4.1 - Prob. 22WECh. 4.1 - Prob. 23WECh. 4.1 - Prob. 24WECh. 4.1 - Prob. 25WECh. 4.1 - Prob. 26WECh. 4.1 - Prob. 27WECh. 4.1 - Prob. 1MRECh. 4.1 - Prob. 2MRECh. 4.1 - Prob. 3MRECh. 4.1 - Prob. 4MRECh. 4.1 - Prob. 5MRECh. 4.1 - Prob. 6MRECh. 4.1 - Prob. 7MRECh. 4.1 - Prob. 8MRECh. 4.1 - Prob. 9MRECh. 4.2 - Prob. 1OECh. 4.2 - Prob. 2OECh. 4.2 - Prob. 3OECh. 4.2 - Prob. 4OECh. 4.2 - Prob. 5OECh. 4.2 - Prob. 6OECh. 4.2 - Prob. 7OECh. 4.2 - 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Prob. 32WECh. 4.2 - Prob. 33WECh. 4.2 - Prob. 34WECh. 4.2 - Prob. 35WECh. 4.2 - Prob. 36WECh. 4.2 - Prob. 37WECh. 4.2 - Prob. 38WECh. 4.2 - Prob. 39WECh. 4.2 - Prob. 40WECh. 4.2 - Prob. 41WECh. 4.2 - Prob. 42WECh. 4.3 - Prob. 1OECh. 4.3 - Prob. 2OECh. 4.3 - Prob. 3OECh. 4.3 - Prob. 4OECh. 4.3 - Prob. 5OECh. 4.3 - Prob. 6OECh. 4.3 - Prob. 7OECh. 4.3 - Prob. 8OECh. 4.3 - Prob. 9OECh. 4.3 - Prob. 10OECh. 4.3 - Prob. 11OECh. 4.3 - Prob. 12OECh. 4.3 - Prob. 13OECh. 4.3 - Prob. 14OECh. 4.3 - Prob. 15OECh. 4.3 - Prob. 16OECh. 4.3 - Prob. 17OECh. 4.3 - Prob. 18OECh. 4.3 - Prob. 1WECh. 4.3 - Prob. 2WECh. 4.3 - Prob. 3WECh. 4.3 - Prob. 4WECh. 4.3 - Prob. 5WECh. 4.3 - Prob. 6WECh. 4.3 - Prob. 7WECh. 4.3 - Prob. 8WECh. 4.3 - Prob. 9WECh. 4.3 - Prob. 10WECh. 4.3 - Prob. 11WECh. 4.3 - Prob. 12WECh. 4.3 - Prob. 13WECh. 4.3 - Prob. 14WECh. 4.3 - Prob. 15WECh. 4.3 - Prob. 16WECh. 4.3 - Prob. 17WECh. 4.3 - Prob. 18WECh. 4.3 - Prob. 19WECh. 4.3 - Prob. 20WECh. 4.3 - Prob. 21WECh. 4.3 - Prob. 22WECh. 4.3 - 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Prob. 16WECh. 4.4 - Prob. 17WECh. 4.4 - Prob. 18WECh. 4.4 - Prob. 19WECh. 4.4 - Prob. 20WECh. 4.4 - Prob. 21WECh. 4.4 - Prob. 22WECh. 4.4 - Prob. 23WECh. 4.4 - Prob. 24WECh. 4.4 - Prob. 25WECh. 4.4 - Prob. 26WECh. 4.4 - Prob. 27WECh. 4.4 - Prob. 28WECh. 4.4 - Prob. 29WECh. 4.4 - Prob. 30WECh. 4.4 - Prob. 31WECh. 4.4 - Prob. 32WECh. 4.4 - Prob. 33WECh. 4.4 - Prob. 34WECh. 4.4 - Prob. 35WECh. 4.4 - Prob. 36WECh. 4.5 - Prob. 1OECh. 4.5 - Prob. 2OECh. 4.5 - Prob. 3OECh. 4.5 - Prob. 4OECh. 4.5 - Prob. 5OECh. 4.5 - Prob. 6OECh. 4.5 - Prob. 7OECh. 4.5 - Prob. 8OECh. 4.5 - Prob. 9OECh. 4.5 - Prob. 10OECh. 4.5 - Prob. 11OECh. 4.5 - Prob. 12OECh. 4.5 - Prob. 13OECh. 4.5 - Prob. 14OECh. 4.5 - Prob. 15OECh. 4.5 - Prob. 16OECh. 4.5 - Prob. 17OECh. 4.5 - Prob. 18OECh. 4.5 - Prob. 19OECh. 4.5 - Prob. 20OECh. 4.5 - Prob. 21OECh. 4.5 - Prob. 1WECh. 4.5 - Prob. 2WECh. 4.5 - Prob. 3WECh. 4.5 - Prob. 4WECh. 4.5 - Prob. 5WECh. 4.5 - Prob. 6WECh. 4.5 - Prob. 7WECh. 4.5 - Prob. 8WECh. 4.5 - Prob. 9WECh. 4.5 - Prob. 10WECh. 4.5 - Prob. 11WECh. 4.5 - Prob. 12WECh. 4.5 - Prob. 13WECh. 4.5 - Prob. 14WECh. 4.5 - Prob. 15WECh. 4.5 - Prob. 16WECh. 4.5 - Prob. 17WECh. 4.5 - Prob. 18WECh. 4.5 - Prob. 19WECh. 4.5 - Prob. 20WECh. 4.5 - Prob. 21WECh. 4.5 - Prob. 22WECh. 4.5 - Prob. 23WECh. 4.5 - Prob. 24WECh. 4.5 - Prob. 25WECh. 4.5 - Prob. 26WECh. 4.5 - Prob. 27WECh. 4.5 - Prob. 28WECh. 4.5 - Prob. 29WECh. 4.5 - Prob. 30WECh. 4.5 - Prob. 31WECh. 4.5 - Prob. 32WECh. 4.5 - Prob. 33WECh. 4.5 - Prob. 34WECh. 4.5 - Prob. 35WECh. 4.5 - Prob. 36WECh. 4.5 - Prob. 37WECh. 4.5 - Prob. 38WECh. 4.5 - Prob. 39WECh. 4.5 - Prob. 40WECh. 4.5 - Prob. 41WECh. 4.5 - Prob. 42WECh. 4.5 - Prob. 43WECh. 4.5 - Prob. 44WECh. 4.5 - Prob. 45WECh. 4.5 - Prob. 46WECh. 4.5 - Prob. 47WECh. 4.5 - Prob. 48WECh. 4.5 - Prob. 49WECh. 4.5 - Prob. 50WECh. 4.5 - Prob. 51WECh. 4.5 - Prob. 52WECh. 4.5 - Prob. 53WECh. 4.5 - Prob. 54WECh. 4.5 - Prob. 55WECh. 4.5 - Prob. 56WECh. 4.5 - Prob. 57WECh. 4.5 - Prob. 58WECh. 4.5 - Prob. 59WECh. 4.5 - Prob. 1MRECh. 4.5 - Prob. 2MRECh. 4.5 - Prob. 3MRECh. 4.5 - Prob. 4MRECh. 4.5 - Prob. 5MRECh. 4.5 - Prob. 6MRECh. 4.5 - Prob. 7MRECh. 4.5 - Prob. 8MRECh. 4.5 - Prob. 9MRECh. 4.5 - Prob. 1ECh. 4.5 - Prob. 2ECh. 4.5 - Prob. 3ECh. 4.5 - Prob. 4ECh. 4.6 - Prob. 1OECh. 4.6 - Prob. 2OECh. 4.6 - Prob. 3OECh. 4.6 - Prob. 4OECh. 4.6 - Prob. 5OECh. 4.6 - Prob. 6OECh. 4.6 - Prob. 7OECh. 4.6 - Prob. 8OECh. 4.6 - Prob. 9OECh. 4.6 - Prob. 10OECh. 4.6 - Prob. 11OECh. 4.6 - Prob. 12OECh. 4.6 - Prob. 13OECh. 4.6 - Prob. 14OECh. 4.6 - Prob. 15OECh. 4.6 - Prob. 16OECh. 4.6 - Prob. 1WECh. 4.6 - Prob. 2WECh. 4.6 - Prob. 3WECh. 4.6 - Prob. 4WECh. 4.6 - Prob. 5WECh. 4.6 - Prob. 6WECh. 4.6 - Prob. 7WECh. 4.6 - Prob. 8WECh. 4.6 - Prob. 9WECh. 4.6 - Prob. 10WECh. 4.6 - Prob. 11WECh. 4.6 - Prob. 12WECh. 4.6 - Prob. 13WECh. 4.6 - Prob. 14WECh. 4.6 - Prob. 15WECh. 4.6 - Prob. 16WECh. 4.6 - Prob. 17WECh. 4.6 - Prob. 18WECh. 4.6 - Prob. 19WECh. 4.6 - Prob. 20WECh. 4.6 - Prob. 21WECh. 4.6 - Prob. 22WECh. 4.6 - Prob. 23WECh. 4.6 - Prob. 24WECh. 4.6 - Prob. 25WECh. 4.6 - Prob. 26WECh. 4.6 - Prob. 27WECh. 4.6 - Prob. 28WECh. 4.6 - Prob. 29WECh. 4.6 - Prob. 30WECh. 4.6 - Prob. 31WECh. 4.6 - Prob. 32WECh. 4.6 - Prob. 33WECh. 4.6 - Prob. 34WECh. 4.6 - Prob. 35WECh. 4.6 - Prob. 36WECh. 4.6 - Prob. 37WECh. 4.6 - Prob. 38WECh. 4.6 - Prob. 39WECh. 4.6 - Prob. 40WECh. 4.6 - Prob. 41WECh. 4.6 - Prob. 42WECh. 4.6 - Prob. 43WECh. 4.6 - Prob. 44WECh. 4.6 - Prob. 45WECh. 4.6 - Prob. 46WECh. 4.6 - Prob. 47WECh. 4.6 - Prob. 48WECh. 4.6 - Prob. 49WECh. 4.6 - Prob. 50WECh. 4.6 - Prob. 51WECh. 4.6 - Prob. 52WECh. 4.6 - Prob. 53WECh. 4.6 - Prob. 54WECh. 4.6 - Prob. 55WECh. 4.6 - Prob. 56WECh. 4.6 - Prob. 57WECh. 4.6 - Prob. 58WECh. 4.6 - Prob. 59WECh. 4.6 - Prob. 1STCh. 4.6 - Prob. 2STCh. 4.6 - Prob. 3STCh. 4.6 - Prob. 4STCh. 4.6 - Prob. 5STCh. 4.6 - Prob. 6STCh. 4.6 - Prob. 7STCh. 4.6 - Prob. 8STCh. 4.6 - Prob. 9STCh. 4.6 - Prob. 10STCh. 4.6 - Prob. 1ECh. 4.6 - Prob. 2ECh. 4.6 - Prob. 3ECh. 4.6 - Prob. 4ECh. 4.6 - Prob. 5ECh. 4.6 - Prob. 6ECh. 4.7 - Prob. 1OECh. 4.7 - Prob. 2OECh. 4.7 - Prob. 3OECh. 4.7 - Prob. 4OECh. 4.7 - Prob. 5OECh. 4.7 - Prob. 6OECh. 4.7 - Prob. 7OECh. 4.7 - Prob. 8OECh. 4.7 - Prob. 9OECh. 4.7 - Prob. 10OECh. 4.7 - Prob. 11OECh. 4.7 - Prob. 12OECh. 4.7 - Prob. 13OECh. 4.7 - Prob. 14OECh. 4.7 - Prob. 15OECh. 4.7 - Prob. 16OECh. 4.7 - Prob. 17OECh. 4.7 - Prob. 18OECh. 4.7 - Prob. 1WECh. 4.7 - Prob. 2WECh. 4.7 - Prob. 3WECh. 4.7 - Prob. 4WECh. 4.7 - Prob. 5WECh. 4.7 - Prob. 6WECh. 4.7 - Prob. 7WECh. 4.7 - Prob. 8WECh. 4.7 - Prob. 9WECh. 4.7 - Prob. 10WECh. 4.7 - Prob. 11WECh. 4.7 - Prob. 12WECh. 4.7 - Prob. 13WECh. 4.7 - Prob. 14WECh. 4.7 - Prob. 15WECh. 4.7 - Prob. 16WECh. 4.7 - Prob. 17WECh. 4.7 - Prob. 18WECh. 4.7 - Prob. 19WECh. 4.7 - Prob. 20WECh. 4.7 - Prob. 21WECh. 4.7 - Prob. 22WECh. 4.7 - Prob. 23WECh. 4.7 - Prob. 24WECh. 4.7 - Prob. 25WECh. 4.7 - Prob. 26WECh. 4.7 - Prob. 27WECh. 4.7 - Prob. 28WECh. 4.7 - Prob. 29WECh. 4.7 - Prob. 30WECh. 4.7 - Prob. 31WECh. 4.7 - Prob. 32WECh. 4.7 - Prob. 33WECh. 4.7 - Prob. 34WECh. 4.7 - Prob. 35WECh. 4.7 - Prob. 36WECh. 4.7 - Prob. 37WECh. 4.7 - Prob. 38WECh. 4.7 - Prob. 39WECh. 4.7 - Prob. 40WECh. 4.7 - Prob. 41WECh. 4.7 - Prob. 42WECh. 4.7 - Prob. 43WECh. 4.7 - Prob. 44WECh. 4.7 - Prob. 45WECh. 4.7 - Prob. 46WECh. 4.7 - Prob. 47WECh. 4.7 - Prob. 48WECh. 4.7 - Prob. 49WECh. 4.7 - Prob. 50WECh. 4.7 - Prob. 51WECh. 4.7 - Prob. 52WECh. 4.7 - Prob. 53WECh. 4.7 - Prob. 54WECh. 4.7 - Prob. 55WECh. 4.7 - Prob. 56WECh. 4.7 - Prob. 1MRECh. 4.7 - Prob. 2MRECh. 4.7 - Prob. 3MRECh. 4.7 - Prob. 4MRECh. 4.7 - Prob. 5MRECh. 4.7 - Prob. 6MRECh. 4.7 - Prob. 7MRECh. 4.7 - Prob. 8MRECh. 4.7 - Prob. 9MRECh. 4.7 - Prob. 10MRECh. 4.7 - Prob. 11MRECh. 4.7 - Prob. 12MRECh. 4.8 - Prob. 1PCh. 4.8 - Prob. 2PCh. 4.8 - Prob. 3PCh. 4.8 - Prob. 4PCh. 4.8 - Prob. 5PCh. 4.8 - Prob. 6PCh. 4.8 - Prob. 7PCh. 4.8 - Prob. 8PCh. 4.8 - Prob. 9PCh. 4.8 - Prob. 10PCh. 4.8 - Prob. 11PCh. 4.8 - Prob. 12PCh. 4.8 - Prob. 13PCh. 4.8 - Prob. 14PCh. 4.8 - Prob. 15PCh. 4.8 - Prob. 16PCh. 4.8 - 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